Answer:
12, 13, 14
Step-by-step explanation:
Let the smallest of the three integers be x.
The difference between an integer and the next greater one is 1.
Then the next greater one is x + 1, and the greatest one of all is x + 2.
Now we translate each piece of the given information until we find an equation.
"the first increased by twice the second"
x + 2(x + 1)
"is"
=
"24 more than the third"
x + 2 + 24
Put all three pieces together, and you get the equation:
x + 2(x + 1) = x + 2 + 24
Now we solve the equation for x, the smallest of the three integers.
x + 2x + 2 = x + 26
3x + 2 = x + 26
2x = 24
x = 12
The smallest integer is 12.
x + 1 = 12 + 1 = 13
x + 2 = 12 + 2 = 14
The other two integers are 13 and 14.
Answer: 12, 13, 14
Now, we check the answer with the given information.
"the first increased by twice the second"
12 + 2 * 13 = 12 + 26 = 38
The first increased by twice the second is 38.
"24 more than the third"
14 + 24 = 38
24 more than the third one is 38.
38 = 38
Our solution is correct.
